Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment

Maastricht University, School of Business and Economics, RM/16/021

19 Pages Posted: 28 May 2016

See all articles by P. Jean-Jacques Herings

P. Jean-Jacques Herings

Tilburg University

Andrey Meshalkin

Maastricht University - Department of Economics

Arkadi Predtetchinski

Maastricht University

Date Written: May 10, 2016

Abstract

The paper considers a class of decision problems with in_nite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. We introduce the notions of Nash equilibrium, subgame perfect equilibrium, and curb sets for decision problems. An optimal policy at the initial history is a Nash equilibrium but not vice versa. Both subgame perfect equilibria and curb sets are equivalent to subgame optimal policies. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.

Keywords: decision problem, multiple selves, subgame perfect equilibrium, curb sets

JEL Classification: C61, C62, C73

Suggested Citation

Herings, P. Jean-Jacques and Meshalkin, Andrey and Predtetchinski, Arkadi, Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment (May 10, 2016). Maastricht University, School of Business and Economics, RM/16/021, Available at SSRN: https://ssrn.com/abstract=2785592 or http://dx.doi.org/10.2139/ssrn.2785592

P. Jean-Jacques Herings (Contact Author)

Tilburg University ( email )

Department of Econometrics and Operations Research
P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4668797 (Phone)
5000 LE (Fax)

HOME PAGE: http://https://sites.google.com/view/jean-jacques-herings/home

Andrey Meshalkin

Maastricht University - Department of Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

Arkadi Predtetchinski

Maastricht University ( email )

Tongersestraat 53
Maastricht, 6200 MD
Netherlands
+31 43 388 3906 (Phone)

HOME PAGE: http://www.personeel.unimaas.nl/a.predtetchinski/

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